IS-LM Model Equilibrium (PDF)

IS-LM MODEL SESSION 11 PROF. ANKITA DASH Source: Google photos 1  THE IS CURVE The IS curve (“Investment-Savings” curve) shows combinations of interest rates and levels of output such that planned spending equals income We can also derive the IS curve usi...

IS-LM MODEL SESSION 11 PROF. ANKITA DASH Source: Google photos 1  THE IS CURVE The IS curve (“Investment-Savings” curve) shows combinations of interest rates and levels of output such that planned spending equals income We can also derive the IS curve using the goods market equilibrium condition: Y = AD = A + c(1 − t )Y − bi  Y − c(1 − t )Y = A − bi Y (1 − c(1 − t )) = A − bi Y = G ( A − bi ) 1 where G = (1 − c(1 − t )) is the Government multiplier THE IS CURVE  THE LM CURVE The LM schedule shows all combinations of interest rates and levels of income such that the money market is in equilibrium The LM curve can be obtained directly by combining the demand curve for real balances and the fixed supply of real balances – For the money market to be in equilibrium, supply must equal demand: M = kY − hi P – Solving for i: 1 M i =  kY −  h P THE LM CURVE GOODS MARKET AND MONEY MARKET EQUILIBRIUM  EQUILIBRIUM - THE GOODS AND MONEY MARKET The IS and LM schedules summarize the conditions that have to be satisfied for the goods and money markets to the in equilibrium Assumptions: Price level is constant Firms willing to supply whatever amount of output is demanded at that price level EQUILIBRIUM - THE GOODS AND MONEY MARKET  CHANGES IN THE EQUILIBRIUM LEVELS OF INCOME AND THE INTEREST RATE The equilibrium levels of income and the interest rate change when either the IS or the LM curve shifts Figure shows effects of an increase in autonomous spending – Shifts IS curve out by  G I if autonomous investment is the source of increased spending – The resulting change in Y is smaller than the change in autonomous spending due to slope of LM curve CHANGES IN THE EQUILIBRIUM LEVELS OF INCOME AND THE INTEREST RATE  DERIVING THE AD SCHEDULE The AD schedule maps out the IS-LM equilibrium holding autonomous spending ( 𝐴)ҧ and the nominal money supply ( 𝑀) ഥ constant and allowing prices (P) to vary Suppose prices increase from 𝑃1 to 𝑃2 𝑀ഥ 𝑀ഥ – decreases to → LM decreases from 𝐿𝑀1 to 𝐿𝑀2 𝑃1 𝑃2 – Interest rates increase from 𝑖1 to 𝑖2 , and output falls from 𝑌1 to 𝑌2 => Corresponds to lower AD DERIVING THE AD SCHEDULE  DERIVING THE AD SCHEDULE Derive the equation for the AD curve using the equations for the IS-LM curves: IS : Y = G ( A − bi ) 1 M LM : i =  kY −  h P  Substituting LM equation into the IS equation:  b M  Y =  G  A −  kY −   h P  h G b G M = A+ h + kb G h + kb G P bM = A +  h P  DERIVING THE AD SCHEDULE hG bG M Y= A+ h + kbG h + kbG P The above equation is the AD (Aggregate Demand) schedule – It summarizes the IS-LM relation, relating Y and P for given levels of autonomous spending and nominal balances – Since P is in the denominator, AD is downward sloping The above equation shows that AD depends directly upon: 1. Autonomous spending 2. Real money stock Equilibrium income is higher with: – higher level of autonomous spending – higher stock of real balances of money Source: Google photos 15